Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Some simplifications of the proofs of Oka-Cartan theory and a weak coherence theorem

Junjiro Noguchi

created by daniele on 22 Jun 2017

28 jun 2017 -- 11:30

Aula Tricerri, DiMaI, Firenze

Abstract.

In Oka-Cartan-Serre-Grauert theory there are still several points which are not easy in former standard references and textbooks; e.g., the proof of Oka's Coherence Theorems, Cartan's matrix lemma used to obtain Oka's Syzygy and L. Schwartz Finiteness Theorem used to proof Cartan-Serre Theorem and Grauert's proof of Oka's Theorem (IX) (Levi problem). We will discuss the simplifications of those theorems that are easy to read and easy to lecture (not all are my originals). Levi problem was solved by Oka IX published in 1953 for unramified Riemann domains of general dimension, but in fact Oka solved it 1943 in some unpublished research reports written in Japanese. I will talk about the interesting history about the delay of ten years.

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